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Decomposability versus entanglement of quantum states in four dimensions bound by pre-selection of two-dimensional subspaces

Hans Havlicek, Karl Svozil

Published Oct 16, 2020• 1 citation
OpenAlex

Abstract

Criteria for the completion of a given incomplete basis of, or context in, a four-dimensional Hilbert space by (in)decomposable vectors are given.

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The analysis of an open quantum system can be by far difficult if the dimension of the system Hilbert space is large or infinite. However, in some cases the dynamics on a finite-dimensional Hilbert space can be decomposed into a block-diagonal form, which simplifies the system structure. In this presentation, we will study several criteria for the complete reducibility and, in addition, a computational method for a basis of each simplified component to apply for the analysis of open quantum systems. An important point of these tools is that they are “effective” methods (one can complete the task in a finite number of steps).